1. Male or female patient aged 18 years or older 2. Pathologic diagnosis of DLBCL, non-GCB subtype, or MCL 3. Patients with DLBCL must have relapsed or refractory disease and have failed or been intolerant to available standard therapy 4. Patients with MCL must have relapsed or refractory disease and have received at least one prior line of therapy 5. Patients who have received previous CD19-directed therapy must have a biopsy which shows CD19 expression after completion of the CD19-directed therapy 6. Measurable disease as defined by the 2014 Lugano Classification 7. Availability of formalin-fixed paraffin-embedded (FFPE) tumor tissue block (or minimum 10 freshly cut unstained slides if block is not available) Note: Any biopsy since initial diagnosis is acceptable, but if several samples are available, the most recent sample is preferred. 8. ECOG performance status 0 to 2 9. Screening laboratory values within the following parameters: a. Absolute neutrophil count (ANC) e"1.0 × 103/¼L (off growth factors at least 72 hours) b. Platelet count e"75 × 103/¼L without transfusion in the past 7 days c. Hemoglobin e"8 g/dL (4.96 mmol/L), transfusion allowed d. Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and gamma glutamyl transferase (GGT) d"2.5 × the upper limit of normal (ULN), d"5 × ULN if there is liver involvement e. Total bilirubin d"1.5 × ULN (patients with known Gilbert s syndrome may have a total bilirubin up to d"3 × ULN) f. Blood creatinine d"1.5 × ULN or calculated creatinine clearance e"60 mL/min by the Cockcroft and Gault equation Note: A laboratory assessment may be repeated a maximum of two times during the Screening period to confirm eligibility. 10. Negative beta-human chorionic gonadotropin (²-HCG) pregnancy test within 7 days prior to start of study drugs on C1D1 for women of childbearing potential 11. Women of childbearing potential* must agree to use a highly effective** method of contraception from the time of giving informed consent until at least 16 weeks after the last dose of study therapy. Men with female partners who are of childbearing potential must agree that they will use a highly effective method of contraception from the time of giving informed consent until at least 16 weeks after the patient receives his last dose of study therapy * Women of childbearing potential are defined as sexually mature women who have not undergone bilateral tubal ligation, bilateral oophorectomy, or hysterectomy, or who have not been postmenopausal (i.e., who have not menstruated at all) for at least 1 year. ** Highly effective forms of birth control are methods that achieve a failure rate of less than 1% per year when used consistently and correctly. Highly effective forms of birth control include: hormonal contraceptives (oral, injectable, patch, intrauterine devices), male partner sterilization, or total abstinence from heterosexual intercourse, when this is the preferred and usual lifestyle of the patient. Note: The double-barrier method (e.g., synthetic condoms, diaphragm, or cervical cap with spermicidal foam, cream, or gel), periodic abstinence (such as calendar, symptothermal, post-ovulation), withdrawal (coitus interruptus), lactational amenorrhea method, and spermicide-only are not acceptable as highly effective methods of contraception.

1. Known history of hypersensitivity to or positive serum human ADA to a CD19 antibody 2. Known history of hypersensitivity to ibrutinib 3. Previous therapy with ibrutinib or other BTK inhibitors 4. Previous therapy with loncastuximab tesirine 5. Requires treatment or prophylaxis with a moderate or strong cytochrome P450 (CYP) 3A inhibitor 6. Allogenic or autologous transplant within 60 days prior to start of study drugs (C1D1) 7. Active graft-versus-host disease 8. Post-transplantation lymphoproliferative disorder 9. Active autoimmune disease, including motor neuropathy considered of autoimmune origin and other central nervous system (CNS) autoimmune disease 10. Known seropositive and requiring anti-viral therapy for human immunodeficiency (HIV) virus, hepatitis B virus (HBV), or hepatitis C virus (HCV). 11. History of Stevens-Johnson syndrome or toxic epidermal necrolysis 12. Lymphoma with active CNS involvement at the time of screening, including leptomeningeal disease 13. Clinically significant third space fluid accumulation (i.e., ascites requiring drainage or pleural effusion that is either requiring drainage or associated with shortness of breath) 14. Breastfeeding or pregnant 15. Significant medical comorbidities, including but not limited to, uncontrolled hypertension (blood pressure [BP] e"160/100 mmHg repeatedly), unstable angina, congestive heart failure (greater than New York Heart Association class II), electrocardiographic evidence of acute ischemia, coronary angioplasty or myocardial infarction within 6 months prior to screening, uncontrolled atrial or ventricular cardiac arrhythmia, poorly controlled diabetes mellitus, severe chronic pulmonary disease, or tuberculosis infection (tuberculosis screening based on local standards) 16. Major surgery, radiotherapy, chemotherapy, or other anti-neoplastic therapy within 14 days prior to start of study drugs (C1D1), except shorter if approved by the Sponsor 17. Use of any other experimental medication within 14 days prior to start of study drugs (C1D1) 18. Planned live vaccine administration after starting study drugs (C1D1) 19. Any condition that could interfere with the absorption or metabolism of ibrutinib including malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel 20. Inherited or acquired bleeding disorders 21. Ongoing anticoagulation with warfarin or equivalent vitamin K antagonists 22. Failure to recover to Grade d"1 (Common Terminology Criteria for Adverse Events [CTCAE] version 4.0) from acute non-hematologic toxicity (Grade d"2 neuropathy or alopecia) due to previous therapy prior to screening 23. Congenital long QT syndrome or a corrected QTcF interval of >480 ms at screening (unless secondary to pacemaker or bundle branch block) 24. Active second primary malignancy other than non-melanoma skin cancers, non-metastatic prostate cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the breast, or other malignancy that the Sponsor s medical monitor and Investigator agree, and document should not be exclusionary 25. Any other significant medical illness, abnormality, or condition that would, in the Investigator s judgment, make the patient inappropriate for study participation or put the patient at risk